In this paper, the composition principle of kinematic chain (K.C.) with multiple joints (M.J.) is frstly discussed, and a factor of M.J. about kinematic chain with M.J. is defined, so that the structural analysis and synthesis of the K.C. with M.J. could be simplified. The 6-bar and 8-bar Assur groups with M.J. are also investigated. All the independent types of the Assur groups with M.J. are obtained.